Title: A functional data depth based on moments
Authors: Germain Van Bever - Universite de Namur (Belgium) [presenting]
Stanislav Nagy - Charles University (Czech Republic)
Pauliina Ilmonen - Aalto University School of Science (Finland)
Sami Helander - Aalto University School of Science (Finland)
Lauri Viitasaari - University of Helsinki (Finland)
Abstract: The aim is to introduce a new depth concept in the functional setup. The integrated depths make up a large class of depth examples in the functional context, that is, say, in a situation where the observations are functions on some interval $I$. These depth functions typically consist in pointwise integration of (univariate or multivariate) depth values to achieve a global value. Several concepts exist. Consistency of these concepts were also studied. We introduce a new depth, based on moments of the distribution of depth values along $I$ rather than standard integration. We study their universal asymptotic properties and illustrate their usefulness in the classification context. We show that, similar to existing depth concepts, the study of the distribution allows us to take into account variations in location, but also in the shape or roughness of the function.